Question

Is there a relationship between the dollars spent each week on recreation and the number of members of the family? Do larger families spend more on recreation? Ten Chicago families shared the following information:

Family Size               3         6        5        6        6        3        4         4         5        3

Amount Spent          99        104     151     129     142     111     74        91        119     91

a. What is the dependent variable (Y) in this situation?

b. What is the independent variable (X) in this situation?

c. Calculate ∑X, ∑Y, ∑XY, ∑X², and ∑Y².

d. Calculate SS_XX, SS_YY, and SS_XY.

e. Calculate the estimated slope coefficient, b₁.

f. Calculate the estimated y-intercept, b₀.

g. Interpret the estimated slope coefficient.

h. Predict the recreational spending for a family of size 5.

i. If there are families of that size in the data set, what are the residuals for those observations?

j. Test the explanatory power of the model at a 5% level of significance.

k. Test if there is a positive relationship between family size and recreational spending. Use alpha = 0.01.

l. What is the excel command used to produce the p-value associated with the test in part k?

Answer 1